Question

Benjamin and his children went into a movie theater and will buy bags of popcorn

and candies. Each bag of popcorn costs $6 and each candy costs $3.50. Benjamin has
a total of $60 to spend on bags of popcorn and candies. Write an inequality that
would represent the possible values for the number of bags of popcorn purchased, b,
and the number of candies purchased, c.

Answer 1

The inequality that represents the possible values for the number of bags of popcorn and candies Benjamin can purchase with a budget of $60 is 6b + 3.50c ≤ 60.

Step-by-step explanation:

To represent the possible number of bags of popcorn, b, and candies, c, that Benjamin can purchase with a total of $60, we use the following inequality:

6b + 3.50c ≤ 60

Here, $6 is the cost of one bag of popcorn, and $3.50 is the cost of one candy. Benjamin's budget of $60 is the constraint for the total spending on popcorn and candies. Each term (6b and 3.50c) represents the total cost of the popcorn and candies, respectively, and the sum of these costs must be less than or equal to the total budget of $60.

The inequality shows the tradeoff Benjamin faces when choosing between bags of popcorn and candies, similar to how the budget constraint in the references illustrate tradeoffs between other goods.